Convergence, error analysis and longtime behavior of the scalar auxiliary variable method for the nonlinear Schrodinger equation

We carry out the convergence analysis of the scalar auxiliary variable (SAV) method applied to the nonlinear Schrodinger equation, which preserves a modified Hamiltonian on the discrete level. We derive a weak and strong convergence result, establish second-order global error bounds and present longtime error estimates on the modified Hamiltonian. In addition, we illustrate the favorable energy conservation of the SAV method compared to classical splitting schemes in certain applications.

Automated summary

This article carries out the convergence analysis of the scalar auxiliary variable method applied to the nonlinear Schrodinger equation. It presents weak and strong convergence results and provides error estimates and comparisons on energy conservation.